Modeling Sewer Pipe Deterioration for Risk Based Planning using a Markov Chain Model. Christopher Pawlowski Shawn Loew

Transcription

1 Modeling Sewer Pipe Deterioration for Risk Based Planning using a Markov Chain Model Christopher Pawlowski Shawn Loew August 27, 2014

2 Asset Management Using Risk Based Planning Limited Funds Unlimited Needs Risk Based Decision Support to Do More With Less Do Nothing Repair Replace Page 2

3 Risk Framework RISK = Consequence of Failure X Probability of Failure Consequence Probability Page 3

4 Consequence of Failure Economic Environmental Social Low High Page 4

5 Probability of Failure Failure Hydraulic Level of Service Structural Condition Failure Event Page 5

6 Failure Models 1 Deterministic: Based on fixed relationships, ignore uncertainty Empirical or Physical Statistical: Take into account uncertainty in relationships Probit Regression Markov Chain Bayesian belief networks Physical Probabilistic Consider failure modes and uncertainty Soft Computing Neural Network Fuzzy Logic 1 Marlow, David, et al. "Remaining Asset Life: A State of the Art Review." Water Environment Research Foundation. Alexandria (2009) Page 6

7 Failure: Structural Condition Condition grades or states defined NASSCO PACP Condition Grade Rating Failure 2 1 Excellent Unlikely 2 Good Unlikely for 20 years 3 Fair May fail in years 4 Poor Probably fail in 5-10 years 5 Attention Required Likely fail within 5 years 2 CS Feeney et al. White Paper on Condition Assessment of Wastewater Collection Systems. USEPA publication EPA/600/R-09/049 Page 7

8 Risk Matrix Structural Condition Risk guides response based on asset Consequence of failure Probability of failure Consequence No Action Monitor every 20 yrs Monitor every 10 yrs Monitor every 5 yrs Action Required Probability of Failure Page 8

9 Markov Models Transitions between states are governed by probabilities Markov property: Next state depends on current state only Transition probabilities can be homogeneous or nonhomogeneous in time Semi-Markov models allow time spent in a state to be probabilistic Allows for a greater flexibility when matching data Page 9

10 Simple Markov Chain Model From To P12 P P23 P P34 P P45 P Segments can remain in current state or move to a worse state (unless there is an intervention) Segments cannot jump more than one state at a time Time step must be appropriately short Transitions in time given by simple matrix multiplication Page 10

11 Data Limitations Longitudinal surveys (repeated condition data) of individual pipes are rare Use data over entire population Historical data often lacking, or hidden introduces bias Keep data on pipes replaced in past! Early repairs often not recorded When did condition change? (left censored data) Pipes replaced before fully aging (right censored data) Page 11

12 Data Preparation Group pipes into similar cohorts Size, Material, Soils, etc. Partitioning limited by size of data set Take into account repairs/rehabilitation! Want natural deterioration rate Find most recent condition rating prior to any intervention Page 12

13 Calibration Condition and age data for 1569 pipes out of 2055 Calibration set of 1053 Validation set of 516 (1/3 of total) From To Page 13

14 Calibration Validation Data Model Number of Segments State 1 State 2 State 3 State 4 State 5 Decade Since Construction Page 14

15 Applications Project Condition Grade into Future Current System Conditions: 35% Condition Grade 1 25% Condition Grade 2 17% Condition Grade 3 14% Condition Grade 4 9% Condition Grade 5 In 100 Years 5% Condition Grade 1 8% Condition Grade 2 9% Condition Grade 3 25% Condition Grade 4 53% Condition Grade 5 Proportion of Pipes Predicted Deterioration Age, Years Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Page 15

16 Applications Project Intervention Strategy into Future Rehabilitate 10% of Grade 4, 5 pipes per year Steady State Conditions: 43% Condition Grade 1 29% Condition Grade 2 20% Condition Grade 3 7% Condition Grade 4 1% Condition Grade 5 Proportion of Pipes Predicted Deterioration Grade 1 Grade 2 Grade 3 Grade 4 Grade Age, Years Page 16

17 Applications Risk Costing Monetize Risk Pipe failure carries a cost premium For rehabilitation itself Attendant impacts of failure Consequence Cost Premium % 4 30% 5 50% Page 17

18 Applications Risk Costing Year Present Value Factor Annualized Inspection Cost Probability of Failure Premium Replacement Cost Risk Cost 1 1 $1,000 1% $100,000 $2, $1,000 1% $100,000 $1, $1,000 1% $100,000 $1,522 Annual Risk Cost = Present Value Factor*(Annualized Inspection Cost + Probability of Failure*Premium Replacement Cost) Total Risk Cost = Sum of annual risk costs Page 18

19 Applications Risk Costing Add a Failure state (Emergency Repair Necessary) Pipes in condition grade 4 have 5% chance of failing in a given year, 50% chance in years Pipes in condition grade 5 have 10% chance of failing in a given year, 50% in 6-7 years To From Fail Fail Page 19

20 Applications Risk Costing Pipe failure carries a cost premium Project expected cost of failure over 20 years Average cost under given probabilities Millions $60 $50 $40 $30 $20 Present Value Expected Cost of Emergency Repairs Do Nothing Rehabilitate Rehabilitate for $15 million $10 $ Avoid $35 million in expected risk Years Net Present Value of $20 million Page 20

21 Applications Risk Matrix Is risk matrix consistent with risk cost approach? If inspection cost is high enough, rehab action can be worth it For each cell, vary inspection cost as % of rehab cost and determine how high % must be to make rehab cost effective Consequence No Action Monitor every 20 yrs Monitor every 10 yrs Monitor every 5 yrs Action Required Probability of Failure Page 21

22 Applications Risk Matrix Is risk matrix consistent with risk cost approach? If inspection cost is high enough, rehab action can be worth it For each cell, vary inspection cost as % of rehab cost and determine how high % must be to make rehab cost effective Consequence 5 >66.0% >49.3% >6.5% Rehab No Action 4 8 >44.5% >12.7% Rehab >13.0% >5.0% >24.1% Monitor every 20 yrs Monitor every 10 yrs Monitor every 5 yrs Action Required Probability of Failure Page 22

23 Summary A risk based approach to asset management requires information on probability of failure Although many approaches to modeling structural failure exist, the Markov chain is simple, intuitive and easily applied Good data is key Be aware of data biases Keep historical data Take into account previous repairs Group data into cohorts if possible Failure model especially effective in a risk cost framework Allows investigation of future rehabilitation strategies and costs Page 23

24 Thank You Acknowledgements: Metropolitan Sewer District of Greater Cincinnati August 27, 2014